If $a^{x} = b^{y} = (a b)^{x y}$ , then $x + y$ = ____

0

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x y

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(a b)^{x + y}

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a b

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Solution

The correct option is A $0$
$a^{x} = b^{y} = (a b)^{x y}$
$\Rightarrow a^{x} = a^{x} b^{y}$
As $a^{x} = b^{y}$
$\Rightarrow a^{x} = a^{x} \times a^{x}$
$\Rightarrow a^{x} = 1 = a^{0}$
$\Rightarrow x = 0$
$b^{y} = 1 = b^{0}$
$\Rightarrow y = 0$
$\Rightarrow x + y = 0$

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